The well-known Stein--Tomas restriction theorem gives the sharp range of $p$ for which $L^p\to L^2$ restriction estimates hold for the surface measure on the sphere. This was generalised to arbitrary measures satisfying certain Fourier decay and Frostman conditions by Mockenhaupt, Mitsis, and Bak--Seeger, with the most general version now a fundamental result in harmonic analysis. The Frostman condition essentially asks for uniform control on the measure of small balls and is the endpoint of a continuum of more nuanced conditions which describe the local fluctuations of the measure. This analysis gives rise to the $L^q$-dimensions of a measure and these are a central concept in fractal geometry and a crucial tool in multifractal analysis and the theory of large deviations. In this paper we prove a new Fourier restriction theorem which uses the $L^q$-dimensions instead of the Frostman condition, thus providing a continuum of estimates which recover Stein--Tomas at the endpoint. Our proof gives the endpoint estimate for all values of $q\in(1,\infty]$ via Stein's complex interpolation. In particular, in the case $q=\infty$ this partially resolves a question raised by Bak and Seeger. We explore when our theorem improves on Stein--Tomas, that is, when the range is not optimised at $q=\infty$, and show that this is the case quite generally, including for certain Mandelbrot cascade measures and measures with multifractal behaviour. On the way to proving our main theorem we obtain a novel description of the $L^q$-dimensions based on certain convolution norms, which may be of interest in its own right.

In 1992, Pukhlikov and Khovanskii provided a description of the cohomology ring of toric variety as a quotient of the ring of differential operators on spaces of virtual polytopes. Later Kaveh generalized this construction to the case of cohomology rings for full flag varieties. In this paper we extend Pukhlikov-Khovanskii type presentation to the case of K-theory of toric and flag varieties. First, we study the Frobenius algebras obtained as quotients of the group algebra of free abelian group (possibly of infinite rank). Then we apply this construction to define a K-ring associated to a linear family of (virtual) polytopes. We study in detail two examples of such families: the family of integer (virtual) polytopes with a fixed normal fan and the family of (virtual) Gelfand-Zetlin polytopes. We show that the K-theory of toric and flag varieties can be realized as K-rings of the above families and use this to get natural set of relations in the above K-rings. Further, we describe the classes of structure sheaves of toric orbit closures and Schubert varieties in type A flag varieties. Finally, we show that our results also hold true in T-equivariant setting.

We survey the dimension theory of sets of real numbers with regular continued fraction expansion restricted to a non-empty and possibly infinite subset $\mathcal{D}\subset\mathbb{N}$.

We give an alternative presentation of the small version of the reflection equation algebra associated to $GL_N$ at both odd and even roots of unity, and use our presentation to classify its irreducible representations. We then describe a family of algebras generalizing the small reflection equation algebra, and consider their application to the study of module categories over $U_q(sl_N)$ fusion categories.

We improve the known upper bound for the extremal number of Berge-$C_4$-free $3$-uniform hypergraphs. More precisely, we prove that every $n$-vertex $3$-uniform hypergraph with no Berge cycle of length four has at most \[ \frac{n^{3/2}}{2+\sqrt2}+O(n) \] hyperedges. This improves the previous best-known leading constant $1/\sqrt{10}$ to $1/(2+\sqrt2)$.

We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. sub-Gaussian samples and communicate a limited number of bits to a central server. While Rahmani et al. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required communication and sample complexity. In contrast to the horizontal-split setting, where Braverman et al. [2016] showed that sparsity does not reduce communication cost for mean estimation, we prove that sparsity does help for cross-covariance estimation in the vertical split. Specifically, we establish minimax lower bounds showing that the communication budget per agent scales as $B_k = Ω(σ^4 d_k\, s' \log(d_1 d_2/s')/\varepsilon^2)$ and the sample complexity for cross-covariance estimation as $m = Ω(σ^4\, s' \log(d_1 d_2/s')/\varepsilon^2)$, where $s' = s \wedge d_{\min}$. For the $1$-sparse case, this yields an exponential improvement from $d_1 d_2$ to $\log(d_1 d_2)$ compared to the dense rate. Our lower bounds are established via Fano's method with an explicit sparse packing using a Varshamov--Gilbert-type argument for signed partial permutation matrices combined with the Conditional Strong Data Processing Inequality of Rahmani et al. [2025]. We show the bounds are tight with a matching achievable scheme, based on covering-net quantization and entry-wise hard thresholding, that attains the $s$-sparse lower bound up to polylogarithmic factors.

We develop a unified DeepONet framework for logarithmically stable infinite-dimensional inverse problems, with inverse acoustic scattering as a model application. The framework is formulated at the operator level by separating the learned inverse map into measurement encoding, finite-dimensional neural approximation, and functional reconstruction components. For inverse maps satisfying a logarithmic stability estimate, we establish quantitative a priori error bounds giving separate estimates for the encoder error, the neural approximation error, and the reconstruction error, thereby characterizing the dependence on the encoder dimension, the network size, and the reconstruction dimension. For comparison, we also record the corresponding Lipschitz-stable estimate arising from the same error decomposition. The abstract theory is then specialized to the recovery of a medium contrast from fixed-frequency far-field measurements. Numerical experiments in two and three dimensions illustrate stable reconstructions under measurement noise.

We establish an equivalence between the existence of Costas polynomials and the existence of a special kind of orthomorphism such that their compositions are also orthomorphisms. Computations are easier over these orthomorphisms. We provide a lower bound for the number of Costas polynomials and derive some of their properties. We show that Costas polynomials, by virtue of being multiplicative analogs of planar polynomials, can also be used to construct complete families of mutually orthogonal Latin squares.

We prove the lack of selection in the zero-noise limit for solutions to SDEs driven by a divergence-free, Hölder continuous vector field with exponent $α\in(0,1)$, arbitrarily close to $1$ but fixed. The result applies to a broad class of regularizing additive noises, including fractional Brownian motion and stable Lévy processes. The proof combines pathwise Lagrangian arguments, based on the analysis of the deterministic flows associated to mixing velocity fields, with probabilistic estimates coming from the stochastic sewing lemma. This allows to show that lack of selection happens simultaneously on a large set of initial data, whose complement has arbitrarily small Lebesgue measure.

In this paper, we develop an inferential framework with sharp asymptotic optimality guarantees for Ising models on inhomogeneous random graphs in the subcritical parameter regime. We begin by characterizing the asymptotic distribution of the maximum likelihood (ML) estimate of the natural parameter, based on a single sample from the underlying model, covering both sparse and dense network regimes. Next, to overcome the computational intractability of the ML method, we propose a simple closed-form estimate obtained from a one-step approximation to the likelihood equation. We show that this estimate attains the same asymptotic distribution and variance as the ML estimate, thereby yielding a computationally efficient and asymptotically valid confidence interval for the natural parameter. We complement these inferential results by establishing a Hájek--Le Cam-type local asymptotic minimax theorem, showing that the proposed estimate achieves the smallest possible asymptotic maximum risk, both in rate and in leading constant, over shrinking neighborhoods of the true parameter. We also derive the corresponding limit of experiments. To the best of our knowledge, these are among the first sharp asymptotic optimality results for network-dependent data. Finally, we study goodness-of-fit testing for the natural parameter, deriving the local power of the likelihood ratio test and minimax detection rates. Our analysis relies on new fluctuation results for the sufficient statistic (Hamiltonian) and for the random partition function of Ising models on inhomogeneous random graphs, which are of independent interest.

We study an inverse source problem for the Monge--Ampere equation \[ \det D^2u=f(x) \] on a bounded smooth uniformly convex domain. In the smooth classical regime, we prove that the Dirichlet-to-Neumann map associated with convex solutions determines the positive source uniquely. The proof uses a family of large boundary values and reduces the inverse source problem to the injectivity of the Euclidean X-ray transform.

This paper provides a (Laurent) polynomial reduction to $q$-holonomic sequences $F_k(q)$. We first characterize Laurent polynomials $\tilde{p}(x)$ such that the product $\tilde{p}(q^k)F_k(q)$ is summable. Then the reduction framework is given to decompose any given Laurent polynomial into a summable part and a remainder with lower degree. Finally, we introduce a power-partible reduction for $q$-holonomic sequences of which the recurrence relation satisfies a certain symmetry condition. The advantage is that it can not only simultaneously eliminate the highest-degree and lowest-degree terms of a Laurent polynomial satisfying a symmetry condition, but also guarantee the symmetry of the remainder. As applications, we apply the reduction to $q$-central-Delannoy numbers to derive new $q$-identities and $q$-congruences.

In a previous paper \cite{BT} we studied the asymptotic behavior of $\| \sum_{k=1}^N a_k X_{n_k}\|_p$ for lacunary sequences $(X_{n_k})$ of random variables in $L_p$ and used the result to give a necessary and sufficient condition for the first alternative in the Kadec-Pełczynski theorem in the case $1\le p<2$. In the present paper we extend this result for nonlinear functionals $f_k (a_1 X_{n_1}, \ldots, a_k X_{n_k})$, establishing a uniform version of the subsequence principle of Aldous \cite{ald}. Moreover, we prove Kadec-Pełczynski type theorems in Orlicz spaces $L_ψ$.

The present work develops the results of the series of papers by Buchstaber and Terzić on the standard actions of the compact torus $T^n = (S^1)^n$ on the complex Grassmann manifolds $G_{n,2}$. In those works, a hyperplane arrangement in $\mathbb{R}^n$ was introduced that determines the chamber decomposition of the hypersimplex $Δ_{n,2}$ for the $T^n$-action on $G_{n,2}$. We introduce a notion of admissible graph for the standard action of the torus $T^n$ on the complex Grassmannian $G_{n,2}$. In terms of admissible graphs, we give a complete inductive description (with respect to $n \ge 4$) of the admissible polytopes in $Δ_{n,2}$, as well as of the toric varieties arising as closures of $(\mathbb{C}^*)^n$-orbits on $G_{n,2}$ under the standard $(\mathbb{C}^*)^n$-action. We consider the $T^n$-equivariant Plücker embedding $G_{n,2} \hookrightarrow \mathbb{C}P^{N_2}$, where $N_2 = \binom{n}{2}-1$. Using admissible graphs, for the considered $T^n$-actions, we describe hyperplane arrangements in $\mathbb{R}^n$ that determine the chambers in $Δ_{n,2}$ for the $T^n$-actions on $G_{n,2}$ and $\mathbb{C}P^{N_2}$. Gel'fand, Kapranov, and Zelevinsky introduced the notions of secondary polytopes and secondary fans in connection with the problem of describing triangulations of a given convex polytope, which is closely related to the Newton polytopes of discriminants and resultants. For the $T^n$-action on $\mathbb{C}P^{N_2}$, we show that the cones in $\mathbb{R}^n$ with vertex at the origin spanned by the chambers form the secondary fan of the cone spanned by the vertices of $Δ_{n,2}$.

The theory of connections is at the very core of differential geometry. Discovered by Levi-Civita and Christoffel and later studied by Cartan, Koszul, and others, connections appear in their most general form under the name of Ehresmann connections. An Ehresmann connection consists of a splitting of the tangent bundle of a submersion into the vertical sub-bundle and a given horizontal distribution. In this paper, we generalize Ehresmann connection to a categorical setting called tangent categories. Initially introduced by Rosický in 1984 and later generalized by Cockett and the first author in 2014, tangent categories provide a categorical framework to study geometry that extends well beyond smooth manifolds, including algebraic geometry and non-commutative geometry. In this paper we introduce and study Ehresmann connections in the context of tangent categories. We give various equivalent formulations in term of full and abstract connections and prove that they generalize Koszul connections. We also define parallel transport and curvature for such connections, and prove the structural equation and the Bianchi identity for the curvature.

Constrained simulation optimization (CSO) is a general framework for optimizing stochastic systems under performance constraints. It arises widely in practice where objective and constraint evaluations are available only through noisy simulation outputs. Compared with the unconstrained setting, the lack of accessible analytical gradients for simulation-based constraints makes it more challenging to develop efficient solution methods and establish non-asymptotic guarantees. To address this gap, we propose a novel single-loop algorithm, called min-max gradient search (MGS), which integrates a primal-dual framework with stochastic gradient estimators. Unlike conventional stochastic approximation methods based on gradient descent for solving simulation optimization problems, such as Zhou and Bhatnagar (2017) and Hu and Fu (2025), MGS performs alternating gradient descent and ascent on the primal and dual variables, which improves the objective while penalizing constraint violations. For the first time, we establish a finite-time convergence guarantee for single-loop CSO algorithms by showing that MGS converges to a stationary solution (a Karush-Kuhn-Tucker point under mild conditions) at a rate of $\tilde{O}(T^{-1/3})$, where $T$ is the number of iterations. Numerical experiments on a serial queuing system and a 2000-dimensional optimization problem demonstrate the superior performance and scalability of MGS.

We study $L^2$-averaged discrepancies of finite sequences of points in the torus $\mathbb{T}^d$ with respect to translated and dilated copies of convex bodies with non-smooth boundary. Under suitable anisotropic assumptions on the decay of the Fourier transform of the body, we prove matching lower and upper bounds for the averaged discrepancy, obtaining the rate $ N^{1 - \frac{d+1}{d^2+d-1}}$. This yields an intermediate regime between smooth convex bodies and polytopes and recovers the known exponent $2/5$ in dimension $d=2$. The argument relies on harmonic analysis techniques combined with averaging procedures adapted to the anisotropic setting. As an application, we analyze a class of convex bodies exhibiting mixed geometric features, including flat regions, curved parts, and edges.

In this article, a new type of multiple access, termed Environment-Division Multiple Access (EDMA), is introduced and its interaction with AI-native communication networks is illustrated. In particular, the key properties of EDMA, such as utilizing the features of wireless propagation environments, integrating advanced flexible antennas, and proactively reconfiguring propagation environments, are described. The article also illustrates two types of applications of AI tools to multiple access, namely AI-assisted EDMA and AI-native EDMA. Finally, open problems and important directions for future research in AI-assisted EDMA are discussed.

We introduce new contraction conditions based on classical inequality between arithmetic and geometric means. By incorporating an auxiliary semimetric $δ$, we define arithmetic-geometric mean, multiplicative-type, and additive-type contractions. Connections between these types of contractions are found. Fixed point theorems are proved in the case of continuity of the above mentioned contractions. Under suitable regularity conditions on $δ$ (such as being d-regular, strongly d-regular, or d-lower bounded) we obtain constructive corollaries. Various examples demonstrating our results are constructed. It is shown that with certain caveats fixed point theorem for additive-type mappings is equivalent to the fixed point theorem for perturbed metric spaces, which were recently introduced by M. Jleli and B. Samet.

We provide sufficient conditions for comparing $m$-generalized order statistics with respect to the increasing concave, increasing convex, and star-shaped stochastic orders. These conditions allow us to rank classical order statistics, selected censored type-II order statistics, and records. They depend on both the parameters of the generalized order statistics and the underlying distribution. Rather than assuming a specific parametric form, we adopt a nonparametric approach and assume some stochastic transform-ordered property, that is, some suitable shape condition. This framework encompasses many relevant classes of distributions that are related, via transform order, to the generalized and the negative generalized Pareto distribution.

We study the semilinear wave equation $ V(x) \partial_t^2 u + d(t) M(x,\nabla_x) u=\tilde{V}(x) \tilde{d}(t) |u|^{p-1}u$ on $ \mathbb{R}^N \times \mathbb{R}$ and show the existence of solutions which are localized in space and in time, called rogue waves, by means of variational methods. We introduce an energy functional on a suitable Hilbert space, and provide sufficient conditions on the coefficients $V, \tilde{V}, d, \tilde{d}$, the elliptic operator $M$ and $p>1$ for the existence of a critical point. Our approach is based on a detailed analysis of the wave type operator and in particular its spectral properties. Further regularity considerations show that critical points are weak solutions to our equation. Moreover, we provide examples of the coefficients and the elliptic operator which satisfy our assumptions.

We construct probabilistic strong solutions to the cubic Schrödinger equation on the three-dimensional ball with radial initial data, which is a significant improvement of a result by Bourgain--Bulut. These solutions lie in the supercritical regime with respect to the probabilistic scaling introduced by Deng--Nahmod--Yue. We achieve this result through gauge transformations that do not modify the equation, combined with a refined modulation analysis using random averaging operators.

Estimating the logarithm of the determinant of large sparse positive definite symmetric matrices is an important task in numerical linear algebra, machine learning, Gaussian processes, and uncertainty quantification. In this work, we introduce two scalable and efficient methods for large-scale log-determinant termed the Optimal Stochastic Arnoldi with Incomplete Orthogonalization Procedure (OSA-IOP) and the Optimal Stochastic Lanczos Quadrature (OSLQ). The OSA-IOP approach extends the Incomplete Orthogonalization Procedure (IOP), originally developed for matrix exponential functions for exponential time stepping integrators, to compute the action of the matrix algorithm on a vector. We observe that combining IOP with a randomized Hutch++ algorithm, the OSA-IOP significantly reduces computational cost while maintaining high accuracy. The OSLQ method estimates log-determinants by coupling Lanczos quadrature with Hutch++ and controlled orthogonalization, leveraging Krylov subspaces as efficient quadrature mechanisms to approximate quadratic forms involving the matrix logarithm. We derive error bounds for both methods. Extensive numerical experiments on large-scale sparse matrices from real-world applications demonstrate the accuracy, robustness, and scalability of the proposed approaches.

For smooth nonconvex-strongly-concave minimax problems, existing second-order methods share a common double-loop structure where the inner maximization is solved to sufficiently high accuracy before each second-order step. First-order methods are often adopted in the inner loops for scalability, but they also undermine the condition-insensitivity of second-order methods, limiting these methods to instances with mild conditioning. To resolve this issue, we propose a novel single-loop framework based on an equivalent regularized minimization reformulation of the original problem. By deriving a new adaptive cubic-quadratic majorization to dynamically absorb the non-Lipschitz components of the reformulated Hessian, we establish a regularized Newton method with robust theoretical guarantees across multiple settings. For deterministic problems, our single-loop method matches the $\mathcal{O}(\varepsilon^{-1.5})$ global iteration complexity of the existing double-loop second-order methods, while automatically achieving a local superlinear rate that is unavailable in existing works due to the inner-loop bottleneck. For the stochastic setting, we achieve $\mathcal{O}(\varepsilon^{-3})$ gradient and $\mathcal{O}(\varepsilon^{-2})$ Hessian complexities by integrating a recursive variance reduction, strictly improving those of the double-loop methods by $\mathcal{O}(\varepsilon^{-0.5})$ factors. In both deterministic and stochastic experiments, our methods significantly outperform the benchmarks, offering substantial speedups over the double-loop methods even under mildly conditioned instances. As a byproduct of our analysis, we close a gap in stochastic second-order methods for nonconvex minimization, where the best known result contains a nontrivial technical issue.

We study the distribution of cokernels of Haar-random matrices over the $p$-adic integers with prescribed zero patterns, motivated by the Cohen--Lenstra heuristics. A central feature of our approach is that the asymptotic cokernel distribution is governed by the reductions modulo $p$ of these matrices, viewed as random matrices over the finite field $\mathbb{F}_p$. For several families of support patterns arising from stair-shaped zero regions, including general stair-shaped patterns, band matrices, and matrices with two symmetric stair-shaped zero regions, we show that convergence of the cokernel distribution to the Cohen--Lenstra distribution is equivalent to an asymptotic nonsingularity condition over $\mathbb{F}_p$. We further propose a conjecture for general support patterns and give examples showing that analogous rank-$r$ criteria fail for $r\ge 1$.

Nikiforov conjectured that, for every fixed $k\ge2$ and all sufficiently large $n$, the unique $n$-vertex $C_{2k+2}$-free graph with maximum adjacency spectral radius is $S^+_{n,k}$, where $S_{n,k}=K_k\vee\overline K_{n-k}$ and $S^+_{n,k}$ is obtained from $S_{n,k}$ by adding one edge inside the independent part. Cioabă, Desai and Tait proved this conjecture for $n\ge k^{O(k)}$. Later, Li and Ning raised the problem of determining the optimal exponent $γ=γ(k)$ such that the same conclusion holds for $n\ge Ω(k^{γ(k)})$. We prove a stronger uniform theorem for Nikiforov's matrices $A_α(G)=αD(G)+(1-α)A(G)$. More precisely, for every $ε>0$ there are constants $C_ε$ and $k_ε$ such that for all $0\leα\le1-ε$, $k\ge k_ε$ and $n\ge C_εk$, every $n$-vertex $C_{2k+2}$-free graph $G$ satisfies $ρ_α(G)\leρ_α(S^+_{n,k})$, with equality if and only if $G\cong S^+_{n,k}$. In particular, the case when $α=0$ answers the problem of Li and Ning in the linear range, and the $A_α$-spectral even-cycle threshold is linear in $k$, uniformly for all $α$ bounded away from $1$. Our proof introduces a weighted rooted Erdős--Gallai type path lemma, which may be of independent interest in Perron-vector methods for spectral extremal graph problems. The same method also yields asymptotically tight $A_α$-spectral bounds for two local forbidden-subgraph families, namely $(K_1\vee P_\ell)$-free graphs and $F_s$-free graphs, where $F_s$ denotes the friendship graph.

We present a differentiable framework for end-to-end mutual information (MI) optimization over linear Gaussian directed acyclic graphs (DAGs). The framework targets network-wide design under global constraints, such as a total transmit power budget, and covers MIMO precoding, amplify-and-forward relays, RIS-aided channels, and branching/merging topologies within a common linear Gaussian model. Its core ingredient is a \emph{K-recursion} that analytically propagates all node-pair covariances along the DAG in topological order, including non-adjacent cross-covariances that are necessary for correctly handling branching and merging paths. The resulting covariances yield a closed-form log-determinant expression for the end-to-end MI as a smooth function of the controllable factors. Complex-valued reverse-mode automatic differentiation on this K-recursion then returns the exact Wirtinger gradient at every controllable factor in a single backward sweep, and projected gradient ascent (PGA) is used to maximize the MI under the global constraints. Because no closed-form gradient expression per topology is required, the same topology-agnostic implementation applies to any linear Gaussian DAG. A single topology-agnostic implementation is applied to four representative DAG classes: single-link MIMO, a diamond DAG, a two-hop AF relay, and input-covariance shaping. The same implementation reaches the classical water-filling optimum in the settings where it is available and yields MI improvements in non-single-link topologies without using topology-specific gradient formulas. A further experiment on a multi-layer Gaussian network (11 nodes, 5 layers) illustrates applicability to nontrivial multi-layer topologies for which no closed-form gradient is available.

Let $K \subset \mathbb{R}^{2}$ be a compact set. For $θ\in S^{1}$, let $\mathrm{Vis}_θ(K) \subset K$ be the visible part of $K$ in direction $θ$. We prove that $\operatorname{dim}_{\mathrm{H}} \mathrm{Vis}_θ(K) \leq \tfrac{3}{2}$ for $\mathcal{H}^{1}$ almost every $θ\in S^{1}$. The previous record was $\operatorname{dim}_{\mathrm{H}}\mathrm{Vis}_θ(K) \leq 11/6 \approx 1.833$, due to D. Dąbrowski. Our main tool is a variant of a recent incidence lower bound theorem due to Cohen, Pohoata, and Zakharov where, roughly speaking, lines have been replaced by rays, and $δ^{\varepsilon}$-separated incidences are replaced by $1$-separated incidences.

Let $(T(n),Ω)$ be the covering of the generalized Kronecker quiver $K(n)$, where $Ω$ is a bipartite orientation. Given a regular Auslander--Reiten component $\cD$ of $\modd(T(n),Ω)$, we introduce two invariants: the width $\cW(\cD)$ and the number of flow modules $b(\cD)$. We show that $\cW(\cD)\geq \frac{b(\cD)+1}{2}$. In particular, we get $\{\cW(\cD)| \cD \text{ is a regular component} \}=\mathbb{N}$.

This paper explores stability dichotomies of thermoelastic Timoshenko-Boltzmann systems with hereditary memory, comparing Fourier's parabolic (no thermal relaxation) and Cattaneo's hyperbolic (with thermal relaxation) heat conduction via semigroup theory and spectral analysis. The Fourier-semigroup achieves exponential stability through the $δ$-condition plus a specific parameter condition, while sole $δ$-condition ensures $1/2$-order polynomial stability. The Cattaneo-semigroup retains this polynomial stability but requires a thermal relaxation-included modified parameter condition for exponential stability. As thermal relaxation time approaches zero, Cattaneo's modified parameter converges to Fourier's, formalizing their asymptotic connection. Results show thermal relaxation alters exponential criteria but preserves polynomial decay, supporting stability analysis under time-dependent thermal loading in structural mechanics.